In election control, a “chair” has the ability to make certain decisions in the structure of the election, with the goal of enabling a given candidate to win. These decisions involve adding, deleting, or partitioning voters or candidates. This paper reports on studies of some missing cases within the control complexity of elections. The studies consider complexity issues in the election systems known as fallback voting and Bucklin voting, resolving three previously missing cases for the former and classifying all but one case of the latter.

The one unclassified case is control by partition of voters, in the so-called destructive, ties-promote setting. The results show that the studied election systems are very broadly resistant to control. In other words, the chair’s task is, for most of the standard types of control attacks, nondeterministic polynomial-time (NP) complete.